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ADVANCES
ISSN: 2053-2733

July 2014 issue

Highlighted illustration

Cover illustration: The mathematical tools used by crystallographers began as abstract models of physical or theoretical structures. As the demand for more powerful tools grows, so grows the demand for sophisticated and fundamental models of crystals and crystalline materials. Clockwise from top left: images from Quiquandon et al. [Acta Cryst. (2014), A70, 229-238], Hyde et al. [Acta Cryst. (2014), A70, 319-337] and Moriera de Oliveira & Eon [Acta Cryst. (2014), A70, 217-228].

advances

research papers


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The temperature dependence of hydrogen Uiso and parent Ueq in the riding hydrogen model is investigated by neutron diffraction, aspherical-atom refinements and QM/MM and MO/MO cluster calculations. Fixed values of 1.2 or 1.5 appear to be underestimated, especially at temperatures below 100 K.

mathematical crystallography

editorial


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The current activities of the IUCr Commission on Mathematical Crystallography are described and the articles in this virtual special issue on mathematical crystallography are introduced.

research papers


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The discrete groups of isometries of the two-dimensional sphere, flat (euclidean) plane and the hyperbolic plane are described and unified using orbifolds. A simple classification schema for orbifolds is proposed that allows systematic exploration of the vast wealth of hyperbolic examples. The article also tabulates space groups that form by decorating simpler triply periodic minimal surfaces with so-called crystallographic hyperbolic orbifolds.

foundations

research papers


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Using a three-dimensional finite element analysis approach, a stress-relaxation mechanism was identified to account for the slow, nonequilibrium dynamics of a composite material observed using X-ray photon correlation spectroscopy.

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The relative frequency of occurrence of staurolite twins is explained by the quasi-restoration of the cationic substructures in terms of the pseudo-eigensymmetry of the corresponding crystallographic orbits.

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It is demonstrated that the ambiguity of determination of two- and three-dimensional crystal structures from an algebraic minimum of error-free intensities increases exponentially with the increasing structure size. This exponential dependence becomes steeper with increasing dimensionality.

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A polytope is called Platonic if it has faces of one kind in every dimension, 0 (vertices), 1 (edges), 2 (faces), …. The three-dimensional Platonic solids/polytopes have been known since antiquity: tetrahedron, octahedron, cube, dodecahedron and icosahedron. Platonic solids in any dimension n < ∞ were identified in the 20th century. In this paper a simple recursive method of decoration of the Coxeter–Dynkin diagram is used to describe the faces of all types and dimensions.

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Using a multiple-common-lines method, the orientations of high- and low-signal diffraction patterns can be accurately recovered.

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Crystallographic data of double antisymmetry space groups are presented.

short communications


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Nonmagnetic, magnetic and toroidal properties are given for all 1601 Aizu species of point-group pairs, highlighting the differences in property coefficients between each pair of groups.

international union of crystallography


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